PRECONDITIONING APPLIED TO EULERIAN–EULERIAN GAS-SOLID FLOW CALCULATIONS WITH VARIABLE DENSITY (original) (raw)
Local preconditioning for Eulerian-Eulerian gas-solid flow calculations with variable gas density is investigated. The performance of simultaneous solution algorithms for low-Mach calculations is strongly related to preconditioning. The gas-solid drag source terms are at the origin of a solid volume fraction and frequency dependency of the mixture speed of sound. Whereas the solid volume fraction dependency of the mixture speed of sound is straightforward to account for in the gas-solid preconditioner, this is not the case with the frequency dependency, the frequency not being an extra calculation variable. The preconditioners used so far in the gas-solid flow literature do not account for or eliminate the frequency dependency of the mixture speed of sound and transfer the problem to the numerical speed of sound. Not accounting for the frequency dependency of the mixture speed of sound in the gas-solid preconditioner results, however, in drastic convergence slow down, even when a fully implicit treatment of the drag source terms is taken. Possible approaches to account for the frequency dependency of the mixture speed of sound in the gas-solid preconditioner are investigated. It is shown that the gas-solid preconditioner does not need to remove the frequency dependency of the mixture speed of sound, but should account for it and be scaled according to the mixture speed of sound at the highest frequency calculated, that is the filter frequency mixture speed of sound, which logically depends on the local mesh resolution. Accounting for the filter frequency mixture speed of sound in the gas-solid preconditioner as good as eliminates the reduction of the convergence speed by the gas-solid drag source terms. The addition of a drag history force to the gas-solid preconditioner to properly rescale frequencies lower than the filter frequency hardly alters the convergence behavior. The convergence speed is determined by propagation at the highest, i.e. filter frequency.
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.